Writing contests can be a good way to get your writing polished and also become more known (especially if you win). Also, if they are held by a magazine then often you end up with a subscription too which is nice. Beware of contests which require anything of you other than the entry fee and also which are not associated with a reputable publishing company or magazine.
Here is a list of contests I've come across or sent stuff in to in the past. Feel free to let me know of any more.
Good luck :)